Linear optimal control of continuous time chaotic systems

Merat, Kaveh; Chekan, Jafar Abbaszadeh; Salarieh, Hassan; Alasty, Aria

doi:10.1016/j.isatra.2014.01.003

Cited by 9 publications

(2 citation statements)

References 30 publications

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“…Recently, several researchers have focused on chaos control [2]. Many nonlinear control techniques have been successfully applied on chaos control and synchronization of different dynamical systems [3][4][5], nonlinear control [6][7], active control and backstepping design [8][9][10], fuzzy logic and adaptive control [11][12], adaptive fuzzy control [13].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Type-2 Fuzzy Second Order Sliding Mode Control for Nonlinear Uncertain Chaotic System

Hendel¹,

Khaber²,

Essounbouli³

2015

IJCSITCE

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Section: Introductionmentioning

confidence: 99%

Adaptive Type-2 Fuzzy Second Order Sliding Mode Control for Nonlinear Uncertain Chaotic System

Hendel¹,

Khaber²,

Essounbouli³

2015

IJCSITCE

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“…dos Santos Rodrigues et al 7 have employed SDRE and time-delayed feedback control methods and compared these two methods in suppressing the chaos of tapping mode AFM. Based on the Riccati equation, Merat et al 8 developed a discrete-time, infinite horizon, suboptimal control algorithm for the chaotic AFM system. Kirrou and Belhaq 9 controlled the AFM instability in noncontact mode, which was under excitation by a harmonic base, in the presence of delayed feedback.…”

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confidence: 99%

Robust nonlinear control of atomic force microscope via immersion and invariance

Keighobadi

Hosseini-Pishrobat

Faraji

et al. 2018

Intl J Robust & Nonlinear

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This paper reports an immersion and invariance (I&I)-based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed-loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov-based analysis of the closed-loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method. KEYWORDSatomic force microscope, chaos, disturbance rejection control, immersion and invariance, output feedback control INTRODUCTIONAtomic force microscopes (AFMs) are useful tools for measuring intermolecular forces in electronics, identification of biological materials, materials science, and semiconductors. The main component of an AFM is a microcantilever with a sharp tip, which is connected to a piezoelectric. A photodiode sensor, which is sensitive to the microcantilever's end position, determines the tip displacement. When the tip approaches the sample substrate, the atomic force interaction changes the dynamics of the AFM tip and, consequently, the whole microscope. The AFMs can operate in different modes including contact, noncontact, and tapping modes. In the contact mode, the tip operates within the range of the repulsive Int J Robust Nonlinear Control. 2019;29:1031-1050.wileyonlinelibrary.com/journal/rnc

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A novel intelligent fast terminal sliding mode control for a class of nonlinear systems: application to atomic force microscope

Rezaie

Nikoo

Rafiee

2017

Int. J. Dynam. Control

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Linear optimal control of continuous time chaotic systems

Cited by 9 publications

References 30 publications

Adaptive Type-2 Fuzzy Second Order Sliding Mode Control for Nonlinear Uncertain Chaotic System

Adaptive Type-2 Fuzzy Second Order Sliding Mode Control for Nonlinear Uncertain Chaotic System

Robust nonlinear control of atomic force microscope via immersion and invariance

A novel intelligent fast terminal sliding mode control for a class of nonlinear systems: application to atomic force microscope

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